Wikipedia indicates that interest mostly started in 1933, and earlier mentions seem pretty dubious. For instance, one of the few claims, from 1871, a least seems to have only been related decades later:
One such sighting occurred in October 1871 or 1872, by a Dr D. Mackenzie of Balnain. [....] Mackenzie sent his story in a letter to Rupert Gould in 1934, shortly after popular interest in the monster skyrocketed.
So is the story entirely a modern creation, or is there at least some mythos surrounding the Loch that dates further back?
Yes and no. In the Life of St. Columba, an account of a 6th-century Scottish saint's life which was written about a century after he died, there's an account of his battle with a monster that lived in the River Ness.
From Chapter 28:
"...he saw some of the inhabitants burying an unfortunate man, who, according to the account of those who were burying him, was a short time before seized, as he was swimming, and bitten most severely by a monster that lived in the water; his wretched body was, though too late, taken out with a hook, by those who came to his assistance in a boat... the monster, which, so far from being satiated, was only roused for more prey, was lying at the bottom of the stream, and when it felt the water disturbed above by the man swimming, suddenly rushed out, and, giving an awful roar, darted after him, with its mouth wide open, as the man swam in the middle of the stream. Then the blessed man observing this, raised his holy hand, while all the rest, brethren as well as strangers, were stupefied with terror, and, invoking the name of God, formed the saving sign of the cross in the air, and commanded the ferocious monster, saying, ‘Thou shalt go no further, nor touch the man; go back with all speed.’ Then at the voice of the saint, the monster was terrified, and fled more quickly than if it had been pulled back with ropes..."
You can see this creature, a roaring mankiller, doesn't have much in common with the modern conception of the monster.
Lake or river monster stories do in fact exist from early medieval Ireland (and consequently Scotland; Ireland's cultural colony) as /u/Prufrock451 describes in the case of St. Columa confronting one in the River Ness, but these only really make sense when placed into a broader context.
Folklorist Dáithí Ó hÓgáin's article 'Moch Amach ar Maidin dé Luain!' Staidéar ar an seanchas faoi ollphiasta i lochanna na hÉireann asserts that the trope of a holy man confronting a water beast and overcoming it with his faith is actually fairly common in early medieval Irish hagiographies. These kinds of stories are so prominent that there is even a tale of St Patrick slaying a monster and dying the lake it lived in (Loch Dearg, 'Red Lake') red with its blood! He argues that this trope is actually the Christianization of a pre-Christian literary trope drawn from oral tradition, where a mighty warrior, not a priest, would overcome a water-beast in combat. We know that such a trope actually existed because it shows up sometimes in the medieval transcriptions of oral sources such as the Metrical Dindshenchas, a giant list of folk-etymologies of Irish place names:
The Barrow, enduring its silence,
that flows through the folk of old Ailbe;
a labour it is to learn the cause whence is called
Barrow, flower of all famous names.
No motion in it made
the ashes of Mechi the strongly smitten [I'm assuming that this is the serpent's name]:
the stream made sodden and silent past recovery
the fell filth of the old serpent.
Three turns the serpent made;
it sought out the soldier to consume him;
it would have wasted by its nature all the kine
of the indolent hosts of ancient Erin.
Therefore Diancecht [a pagan god] slew it:
there was rude reason for clean destroying it,
for preventing it for ever from wasting
above every resort, from consuming utterly.
Known to me is its grave where he cast it,
a tomb without walls or roof-tree;
its evil ashes,–no ornament to the region
found silent burial in noble Barrow.
So there are examples of lake monsters like the Loch Ness monster that appear in early medieval sources, but they aren't examples of people genuinely reporting something inexplicable that they saw. They were always folktales or hagiographic stories based on earlier folktales set in a historic past and featured spiritually or magically powerful champions who kill or banish the creature. This doesn't mean that early medieval people didn't believe that lake monsters actually existed, it indicates that they probably believed that they existed in an earlier time and would have been incredibly rare to come across in one's daily life.